Improving quantification theory (I) by the semi-tensor product method.

Quantification theory (I) provides a kind of multi-ary analysis method for the forecast problem with its criterion variable quantitative and its explanatory variables qualitative. In such a theory, the forecast model is a one-dimensional linear one, which cannot be applied to high-dimension or nonlinear forecast problems. By the matrix semi-tensor product method, this paper improves quantification theory (I) from two aspects: model and dimension. First, based on the algebraic expression of mix-valued logical variables, the forecast problem of one-dimensional criterion variable is investigated, and a new forecast model is presented. Second, we consider the multi-dimension forecast problem, and establish a new multidimension forecast method by using mix-valued logical function vectors. Finally, we give an illustrative example to demonstrate our new results. [ABSTRACT FROM AUTHOR]